"A portion of the material ... appeared, in somewhat different order and form, as Theory of recursive functions and effective computability, volume I ... in 1957."
Topics: Recursive functions, Computable functions
Source: inlibrary
University of Illinois Urbana-Champaign
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205
May 1, 2013
05/13
by
Dershowitz, Nachum; National Science Foundation (U.S.); University of Illinois at Urbana-Champaign. Dept. of Computer Science
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"UIUCDCS-R-79-987"
Topics: Computer programs, Recursive functions
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Topics: Probabilities, Recursive functions
185
185
Jul 6, 2009
07/09
by
Williams, Louis Francis, 1932-
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Manuscript copy
Topics: Recursive functions, Electronic digital computers
Click here to view the University of Florida catalog record
Topics: Adaptive filters, Adaptive signal processing, Recursive functions
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45
Nov 16, 2015
11/15
by
Florentin Smarandache
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In this article we will construct a family of expressions ε (n) .
Topics: recursive functions, degree of the expression
Topics: Sequential machine theory, Recursive functions, Programming languages (Electronic computers)
"Computer science library."
Topics: Programming languages (Electronic computers), Computer algorithms, Recursive functions
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146
Sep 20, 2010
09/10
by
Hagood, Nesbitt W.; Crawley, Edward F
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Viewgraphs on cost averaging techniques for robust control of flexible structural systems are presented. Topics covered include: modeling of parameterized systems; average cost analysis; reduction of parameterized systems; and static and dynamic controller synthesis.
Topics: ECONOMIC ANALYSIS, ROBOTS, ECONOMICS, ECONOMY, POLICIES, THEOREM PROVING, TURING MACHINES,...
An algorithm and a computer program that implements the algorithm that performs recursive hierarchical segmentation (RHSEG) of data have been developed. While the current implementation is for two-dimensional data having spatial characteristics (e.g., image, spectral, or spectral-image data), the generalized algorithm also applies to three-dimensional or higher dimensional data and also to data with no spatial characteristics. The algorithm and software are modified versions of a prior RHSEG...
Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, DATA SYSTEMS, RECURSIVE FUNCTIONS, COMPUTER...
Bibliography: p. 120-123
Topics: Recursive functions, Programming languages (Electronic computers), Formal languages, Unsolvability...
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159
Jul 11, 2010
07/10
by
Russell, C. T.; Coleman, P. J., Jr.; Sonett, C. P
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The program of invited talks at the Third Solar Wind Conference is provided, with a table of contents of the proceedings.
Topics: BINARY MIXTURES, PROBABILITY DENSITY FUNCTIONS, RECURSIVE FUNCTIONS, ALGORITHMS, DISTRIBUTION...
From the bitsavers.org collection, a scanned-in computer-related document. mit :: ai :: aim :: AIM-011
Topics: vector, functions, scanning, recursive, function, subblock, components, program, computation,...
This paper explores the use of abstract data types as a modularization and structuring technique in the design of programs, particularly larger programs including compilers and operating systems. The concepts of type and type definition are discussed. Some data structuring mechanisms are generalized and several simple examples are presented. The examples increase in complexity and conclude with the design of a directory system, illustrating the power of data types as a design tool.
Topics: DTIC Archive, Flon, Lawrence, CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE,...
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201
Jul 11, 2010
07/10
by
Stirn, R. J
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The Schottky barrier photovoltaic converter is suggested as an alternative to the p/n junction photovoltaic devices for the conversion of laser energy to electrical energy. The structure, current, output, and voltage output of the Schottky device are summarized. The more advanced concepts of the multilayer Schottky barrier cell and the AMOS solar cell are briefly considered.
Topics: COEFFICIENTS, LEGENDRE FUNCTIONS, TABLES (DATA), APPLICATIONS OF MATHEMATICS, BOUNDARY VALUE...
H(x), the negative logarithm of the apriori probability M(x), i s Levin's variant of Kolmogorov's complexity of a natural number x. Let alpha(n) be the minimum complexity of a number larger than n, s(n) the logarithm of the apriori probability of obtaining a number larger than n. It was known that s(n) or = alpha(n) or = s(n) + H(s(n)). We show that the second estimate is in some sense sharp.
Topics: DTIC Archive, Gacs,Peter, STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE, *PROBABILITY, *RECURSIVE...
Vector Quantization (VQ) is fast becoming an accepted, if not preferred method for image compression. The VQ performs well when compressing all types of imagery including Video, Electro-Optical (EO), Infrared (IR), Synthetic Aperture Radar (SAR), Multi-Spectral (MS), and digital map data. The only requirement is to change the codebook to switch the compressor from one image sensor to another. There are several approaches for designing codebooks for a vector quantizer. Adaptive Vector...
Topics: NASA Technical Reports Server (NTRS), DATA COMPRESSION, IMAGING TECHNIQUES, RECURSIVE FUNCTIONS,...
In this paper, the authors critically evaluate the classical least- fixedpoint approach towards recursive programs. They suggest a new approach which extracts the maximal amount of valuable information embedded in the programs. The presentation is informal, with emphasis on examples.
Topics: DTIC Archive, Manna, Zohar, Shamir, Adi, STANFORD UNIV CA DEPT OF COMPUTER SCIENCE, *COMPUTER...
Predicates can describe functions; the arguments of the predicates are the input and output parameters of the function. Logic programs describe relationships between objects rather than merely sequential instructions, and it is common for both a function and its inverse to be computable by the same logic program. Given values for some subset of the arguments to a function-describing predicate, one may be able to decide, in general, which of the remaining arguments are computable by the logic...
Topics: DTIC Archive, Sickel,Sharon, CALIFORNIA UNIV SANTA CRUZ INFORMATION SCIENCES, *COMPUTER LOGIC,...
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254
May 23, 2011
05/11
by
Jackson, Michael R. C.; Zhao, Yiyuan; Slattery, Rhond
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Air traffic control automation synthesizes aircraft trajectories for the generation of advisories. Trajectory computation employs models of aircraft performances and weather conditions. In contrast, actual trajectories are flown in real aircraft under actual conditions. Since synthetic trajectories are used in landing scheduling and conflict probing, it is very important to understand the differences between computed trajectories and actual trajectories. This paper examines the effects of...
Topics: ALGORITHMS, ANGULAR ACCELERATION, EIGENVALUES, ATTITUDE (INCLINATION), EIGENVECTORS, LEAST SQUARES...
A very general set of orthogonal polynomials with five free parameters is given explicitly, the orthogonality relation is proved and the three term recurrence relation is found. (Author)
Topics: DTIC Archive, Askey,Richard, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *POLYNOMIALS,...
Many algorithms used for data smoothing, data classification and error detection require the calculation of the distance from a point to the polynomial interpolating its 2n neighbors (n on each side). This computation, if performed naively, would require the solution of a system of equations and could create numerical problems. This note shows that if the data is equally spaced, then this calculation can be performed using a simple recursion formula.
Topics: NASA Technical Reports Server (NTRS), DIFFERENCES, GEOMETRY, RECURSIVE FUNCTIONS, ALGORITHMS,...
Recursive feedback is defined and discussed as a framework for development of specific algorithms and procedures that propagate the time-domain solution for a dynamical system simulation consisting of multiple numerically coupled self-contained stand-alone subsystem simulations. A satellite motion example containing three subsystems (other dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem...
Topics: NASA Technical Reports Server (NTRS), COMPUTERIZED SIMULATION, TIME DOMAIN ANALYSIS, RECURSIVE...
The stability of a recursive estimator process (e.g., a Kalman filter is assured for long time periods by periodically resetting an error covariance P(t.sub.n) of the system to a predetermined reset value P.sub.r. The recursive process is thus repetitively forced to start from a selected covariance and continue for a time period that is short compared to the system's total operational time period. The time period in which the process must maintain its numerical stability is significantly...
Topics: NASA Technical Reports Server (NTRS), STABILITY, STATE ESTIMATION, RECURSIVE FUNCTIONS, COVARIANCE,...
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105
Jul 25, 2010
07/10
by
Chung, Jen-Yao; Liu, Jane W. S.; Lin, Kwei-Ja
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One approach to avoid timing faults in hard, real-time systems is to make available intermediate, imprecise results produced by real-time processes. When a result of the desired quality cannot be produced in time, an imprecise result of acceptable quality produced before the deadline can be used. The problem of scheduling periodic jobs to meet deadlines on a system that provides the necessary programming language primitives and run-time support for processes to return imprecise results is...
Topics: ESTIMATING, INDEPENDENT VARIABLES, LAGRANGIAN EQUILIBRIUM POINTS, PARAMETER IDENTIFICATION,...
A computer program was developed that selects, from a list of candidate functions, the approximating functions and associated coefficients which result in the best curve fit of a given set of numerical data. The advantages of the approach used here are: (1) Multivariable approximations can be performed. (2) Flexibility with respect to the type of approximations used is available. (3) The program is designed to choose the best terms to be used in the approximation from an arbitrary list of...
Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, CURVE FITTING, COMPUTER PROGRAMMING, RECURSIVE...
Let X(1),X(2), ..., X(n) be independent random variables such that P(X(i) = j) = P sub j , j = 1,2, ..., n, sum from j = 1 to n of P sub j = 1 and consider a graph with n nodes numbered 1,2, ..., n and the arcs (i,X(i)), i = 1,2, ..., n. We determine the probability that the above so-called random graph is connected and then develop a recursive formula for the distribution of C, the number of connected components it contains. We also derive expressions for the mean and variance of C. (Author)
Topics: DTIC Archive, Ross,Sheldon M, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *GRAPHS, RANDOM...
The Adam language is an extension of Ada that supports multiway activities, which are cooperative activities involving two or more processes. This support is provided by three new constructs: diva procedures, meet statements, and multiway accept statements. Diva procedures are recursive generic procedures having a particular restrictive syntax that facilitates translation for parallel computers. Meet statements and multiway accept statements provide two ways to express a multiway rendezvous,...
Topics: NASA Technical Reports Server (NTRS), ADA (PROGRAMMING LANGUAGE), PARALLEL PROGRAMMING, RECURSIVE...
A function of three variables is often regarded as inherently simpler than a function of five variables, and there has been much attention given to the nature of complicated functions that can be expressed exactly in various ways in terms of simpler functions. From the viewpoint of computation, however, it is sufficient if a function F can be approximated arbitrarily well by combinations of simple functions. This paper deals with the general structure of this process, and obtains specific...
Topics: DTIC Archive, Buck,R Creighton, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER,...
Theodorsen's circulation function relates lift to downwash in unsteady two dimensional incompressible flow. A continued fraction representation for the circulation function is described. The continued fraction converges and has a particularly simple coefficient pattern.
Topics: NASA Technical Reports Server (NTRS), ASYMPTOTIC SERIES, LEAST SQUARES METHOD, RECURSIVE FUNCTIONS,...
The problem of estimating the prior probabilities q sub k of a mixture of known density functions f sub k(X), based on a sequence of N statistically independent observations is considered. It is shown that for very mild restrictions on f sub k(X), the maximum likelihood estimate of Q is asymptotically efficient. A recursive algorithm for estimating Q is proposed, analyzed, and optimized. For the M = 2 case, it is possible for the recursive algorithm to achieve the same performance with the...
Topics: NASA Technical Reports Server (NTRS), BINARY MIXTURES, PROBABILITY DENSITY FUNCTIONS, RECURSIVE...
From the bitsavers.org collection, a scanned-in computer-related document. mit :: ai :: aim :: AIM-055
Topics: recursive, primitive, scanning, definitions, functions, equation, defined, document, domains,...
Joseph R. Schoenfield Degrees of Unsolvability North-Holland Publishing Company 1971 Acrobat 7 Pdf 3.95 Mb. Scanned by artmisa using Canon DR2580C + flatbed option
Topics: Mathematics, Recursive Functions, Isomorphisms, Algorithms, Degrees, Upper & Lower Bounds,...
The recursion relations that were proposed by W. F. Ford and A. Sidi (Appl. Numer. Math, 4 (1988), pp. 477-489) for implementing vector extrapolation methods are used for devising generalizations of the power method for linear operators. These generalizations are shown to produce approximations to largest eigenvalues of a linear operator under certain conditions. They are similar in form to the quotient-difference algorithm and share similar convergence properties with the latter. These...
Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, EIGENVALUES, RECURSIVE FUNCTIONS, VECTORS...
An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process...
Topics: NASA Technical Reports Server (NTRS), ERROR FUNCTIONS, MATHEMATICAL MODELS, RECURSIVE FUNCTIONS,...
The numerical robustness of four generally applicable, recursive, least-squares-estimation schemes is analyzed by means of a theoretical round-off propagation study. This study highlights a number of practical, interesting insights of widely used recursive least-squares schemes. These insights have been confirmed in an experimental study as well.
Topics: NASA Technical Reports Server (NTRS), ERROR ANALYSIS, ESTIMATES, LEAST SQUARES METHOD, RECURSIVE...
We consider the consecutive k-of-n system in which there are n components linearly ordered. Each component either functions or fails and the system is said to be failed if any k consecutive components are failed. Let r(p) = r(p(1), ..., p(n)) denote the probability that the system does not fail given that the components are independent, component i functions with probability p(i), i = 1, ..., n. The function r(p) is called the reliability function. We study the above system both when the...
Topics: DTIC Archive, Derman,Cyrus, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *PROBABILITY...
Models of the main geomagnetic field are generally represented by a scalar potential gamma expanded in a finite number of spherical harmonics. Very accurate observations of F were used, but indications exist that the accuracy of models derived from them is considerably lower. One problem is that F does not always characterize gamma uniquely. It is not clear whether such ambiguity can be encountered in deriving gamma from F in geomagnetic surveys, but there exists a connection, due to the fact...
Topics: NASA Technical Reports Server (NTRS), GEOMAGNETISM, SCALARS, SPHERICAL HARMONICS, MATHEMATICAL...
Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence...
Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTER PROGRAMS, LINEAR EQUATIONS, PARALLEL...
The inclusion problem for the class of monadic recursion schemes is shown to be undecidable. The proof illustrates the close relationship between monadic recursion schemes and deterministic pushdown automata. The proof is extended to show that both the weak equivalence problem for the class of monadic recursion schemes and the weak equivalence problem for the class of free schemes without identity are undecidable.
Topics: NASA Technical Reports Server (NTRS), COMPUTER PROGRAMMING, MATHEMATICAL MODELS, RECURSIVE...
The paper presents two numerical procedures. The first procedure determines the distribution of the time a customer spends in the waiting line, and the second determines the distribution of the length of a busy period. The service time of a customer may depend on the number of customers previously served in the busy period in which he is served. The results are obtained via recursive numerical integrations. (Author)
Topics: DTIC Archive, Barzily,Zeev, GEORGE WASHINGTON UNIV WASHINGTON D C INST FOR MANAGEMENT SCIENCE AND...
A bisection-tranposition algorithm is described for the recursive computation of the Moore-Penrose inverse of a large matrix. (Author)
Topics: DTIC Archive, Krishnamurthy,E V, MARYLAND UNIV COLLEGE PARK COMPUTER SCIENCE CENTER, *SIGNAL...
This paper studies a generalization of the discrete-time GI/G/1 queueing system. Here, the inter-arrival times are not necessarily identically distributed. A recursive scheme is derived to obtain the joint distribution of the duration of the initial busy period, the duration of the first idle period and the number of customers served during the initial busy period. (Author)
Topics: DTIC Archive, Minh,Do Le, CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES, *QUEUEING THEORY,...
A closed form is discussed that provides an interface between formal specification of problems and the algorithms that solve them. (Author)
Topics: DTIC Archive, Sickel,Sharon, CALIFORNIA UNIV SANTA CRUZ INFORMATION SCIENCES, *PROBLEM SOLVING,...
This paper presents an information theoretic approach to information transmission in computational systems. The effect of constraint on information paths is formalized and a number of inductive techniques are developed for proving the absence of information transmission. Finally, it is shown how ordinary inductive assertions can be used in conjunction with the theory to analyse information paths in sequential programs.
Topics: DTIC Archive, Cohen, Ellis S, CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE,...
Optimum estimation of the states of linear dynamic processes using noise corrupted measurements, commonly referred to as Kalman filtering, requires an exact knowledge of the equations which govern the complete stochastic system. In practical applications, however, these equations depend on parameters which can not be precisely defined. When the parameter uncertainties are sufficiently large, standard filtering techniques can produce inaccurate and inadequate estimates. In this dissertation, two...
Topics: DTIC Archive, Schneider,Calvin Chris , Jr, CALIFORNIA UNIV LOS ANGELES, *KALMAN FILTERING,...
The admissibility of certain nonlocal hidden-variable theories are explained via information theory. Consider a pair of Stern-Gerlach devices with fixed nonparallel orientations that periodically perform spin measurements on identically prepared pairs of electrons in the singlet spin state. Suppose the outcomes are recorded as binary strings l and r (with l sub n and r sub n denoting their n-length prefixes). The hidden-variable theories considered here require that there exists a recursive...
Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, ELECTRON SPIN, ENTROPY, INFORMATION THEORY,...
A recursive technique for modeling and estimating a two-dimensional signal contaminated by noise is presented. A two-dimensional signal is assumed to be an undistorted picture, where the noise introduces the distortion. Both the signal and the noise are assumed to be wide-sense stationary processes with known statistics. Thus, to estimate the two-dimensional signal is to enhance the picture. The picture representing the two-dimensional signal is converted to one dimension by scanning the image...
Topics: NASA Technical Reports Server (NTRS), IMAGE ENHANCEMENT, RECURSIVE FUNCTIONS, SIGNAL PROCESSING,...
The classical method for constructing the least fixedpoint of a recursive definition is to generate a sequence of functions whose initial element is the totally undefined function and which converges to the desired least fixedpoint. This method, due to Kleen, cannot be generalized to allow the construction of other fixedpoints. This paper presents an alternate definition of convergence and a new fixedpoint access method of generating sequences of functions for a given recursive definition. The...
Topics: DTIC Archive, Manna, Zohar, STANFORD UNIV CA DEPT OF COMPUTER SCIENCE, *FUNCTIONAL ANALYSIS,...
The recursive algorithm is a polynomially bounded nonsimplex method for solving assignment problems. It begins by finding the optimum solution for a problem defined from the first row, then finding the optimum for a problem defined from rows one and two, etc., continuing until it solves the problem consisting of all the rows. It is thus a dimension expanding rather than an improvement method such as as the simplex. During the method the row duals are non-increasing and the column duals...
Topics: DTIC Archive, Thompson,Gerald L, CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH...